JERUSALEM — At least one rocket fired from the Sinai Peninsula in Egypt struck the southern Israeli resort city of Eilat overnight, causing alarm but no injuries, police officials said on Thursday.

Residents reported hearing several explosions shortly after midnight, and bomb-disposal experts located one rocket that fell in an open area close to buildings in a residential neighborhood.

Israeli security officials have been warning for some time about a growing threat from Sinai. They point to an erosion of Egyptian authority there, particularly in the year since the Egyptian revolution, and to increased efforts by Palestinian militant groups emanating from Gaza to use the vast expanses of desert as a staging ground for a new front against Israel. The rocket attack came just before the Passover holiday, traditionally one of the busiest seasons in Eilat, which is popular with Israeli and foreign tourists.

Prime Minister Benjamin Netanyahu said on Thursday that the Sinai Peninsula “has become a terrorism zone.”

“We are dealing with this. We are building a security fence, but it will not stop missiles,” he said. He added, “We will strike at those who attack us.”

Last August, eight Israelis were killed in a cross-border terrorist attack when gunmen and bombers ambushed a bus and several vehicles on a road just north of Eilat. The attackers’ identities were never established, but Israel blamed a small Palestinian militant group, the Popular Resistance Committees, based in Gaza, for the attack.

In August 2010, a number of rockets were fired from Sinai toward Eilat. One landed across the Jordanian border, striking the Red Sea resort of Aqaba and killing a Jordanian taxi driver.

An Israeli airstrike on Gaza last month killed the leader of the Popular Resistance Committees and his assistant. The military described the killings as a pre-emptive strike timed to thwart another attack being planned against Israelis from across the Egyptian border.

Israel is now rushing to complete a 150-mile, 16-foot-tall steel border fence that will stretch all the way from Eilat up to Gaza.

The unrest comes at a time when Israel’s 30-year peace with Egypt is under strain, after the ouster of President Hosni Mubarak, a former staunch Israeli ally, and the rise of Islamist political forces in Cairo. Israeli officials say that militant groups backed by Iran are trying to undermine Israeli-Egyptian relations further, perhaps by trying to drag Israel into the Sinai Peninsula, and that their actions could have strategic consequences.

“The Popular Resistance Committees is small, but it is financed by Iran,” Amos Gilad, a senior Israeli defense official, said this week. Briefing diplomats and reporters at the Jerusalem Center for Public Affairs, a research institute, Mr. Gilad said that aside from wanting to kill Israelis, “they want to complicate our relations with Egypt. This is their main goal.”

After the cross-border attack in August, Israeli forces killed three of the assailants who had crossed into Israeli territory, and five Egyptian officers were accidentally killed by Israeli security forces as they chased down the attackers. Enraged Egyptians then ransacked the Israeli Embassy in Cairo.